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In this letter, we provide analytical and numerical evidence that the single-layer Quantum Approximate Optimization Algorithm (QAOA) on universal Ising spin models produces thermal-like states with Gaussian perturbations. We find that these pseudo-Boltzmann states can not be efficiently simulated on classical computers according to state-of-art techniques, and we relate this distribution to the optimization potential of QAOA. Moreover, we observe that the temperature depends on a hiddenarXiv:2201.03358v2 fatcat:7wschr6ph5f27lrvrtxnxay6fy